Terminology • Two Different Quantities: Chapter 19: – Electric Potential and Electric Potential Energy • Electric Potential = Voltage Electric Potential & • Note: We will start by considering a point charge, section 18-3. Potential Energy Brent Royuk Phys-112 Concordia University 2 Electric Potential Energy Electric Potential U • Consider two point charges separated by a • Definition: V = distance r. The energy of this system is q o kq q U = o – This is called the electric potential (which r shouldn’t be confused with electric potential • To derive this, you need to integrate work energy), the potential, or the voltage. € using Coulomb’s Law. – Remember: potential is energy per charge. • Potential energies are always defined relatively. • Units Where€ is U = 0 for this system? – In MKS, energy/charge = Joule/Coulomb = 1 • What is negative energy? volt (V) • This is a scalar quantity. • In everyday life, what’s relevant about this • The Superposition Principle applies. infinity stuff? Nothing, really. • We are most often interested in changes and – Potentials tend to be differences. One differences, rather than absolutes. commonly chosen zero: the earth. 3 4 Comparisons Electric Potential • An Analogy • For a point charge, – Coulomb Force --> Electric Field U kqq kq (Force per charge), as V = = o = q rq r – Electric Potential Energy --> Electric o o Potential (Energy per charge) • How is electric potential energy similar to gravitational potential energy? • Potential in this chapter compared to € future chapters. 5 6 1 Electric Potential Examples Electric Potential Examples • A battery-powered lantern is switched on for 5.0 • How much work is required to assemble the minutes. During this time, electrons with total charge charge configuration below? -8.0 x 102 C flow through the lamp; 9600 J of electric potential energy is converted to light and heat. Through what potential difference do the electrons move? • Find the energy given to an electron accelerated through a potential difference of 50 V. – a) The electron volt (eV) 2 3 • An electron is brought to a spot that is 12 cm from a point charge of –2.5 µC. As the electron is repelled away, to what speed will it finally accelerate? 1 4 • Find the electric field and potential at the center of a square for positive and negative charges. – What do positive and negative voltages mean? – E-field lines point in the direction of decreasing V. 7 8 Electric Potential Examples Potential in a Uniform Field • Consider the three charges shown in the figure • Let’s let an electric field do some work below. How much work must be done to move as we move a test-charge against the the +2.7 mC charge to infinity? field: • The work done by the field is: W = -qoEd • Assuming we start at the U = 0 point, we get U = -W = qoEd • Signs? See next slide. • Using the definition of the potential we get: V = Ed 9 10 Potential in a Uniform Field Potential in a Uniform Field • Sign considerations: • Work done by the field is negative, which makes the potential energy positive (useful). – Compare with gravity: 11 12 2 Potential in a Uniform Field Equipotential Surfaces • Example: A uniform field is • An equipotential surface has the established by connecting the same potential at every point on plates of a parallel-plate capacitor the surface. to a 12-V battery. a) If the plates are separated by 0.75 cm, what is • Equipotential surfaces are the magnitude of the electric field perpendicular to electric field lines. in the capacitor? b) A charge of – The electric field is the gradient of +6.24 µC moves from the positive the equipotential surfaces. plate to the negative plate. How • How are equipotential lines much does its electric potential oriented to the surface of a energy change? conductor? 13 14 Equipotential Surfaces Equipotential Surfaces • Comparative examples: – Isobars on a weather map. – Elevation lines on a topographic map. 15 16 Capacitors Capacitors in Circuits • A plate capacitor • Series • It takes energy to charge the plates – Charge is same on all capacitors – Voltage drops across the capacitors – Easy at first, then harder – So V = V1 + V2 + V3 +... Q Q Q Q • Q = CV = + + + ... – Since V = Q/C, C C C C eq 1 2 3 – C is the capacitance – Therefore: 1 1 1 1 – Bigger C means more charge per volt, bigger charge = + + + ... € storage device Ceq C1 C2 C3 • Parallel – 1 farad (F) = 1 coulomb/volt – The voltage is the same across all capacitors. ε A • C = o Different amounts of charge collect on each d € -12 2 2 capacitor – εo = 8.85 x 10 C /Nm (permittivity of free space) – Q = Q + Q + Q +... – Connect with k 1 2 3 – Q = CV, so CeqV = C1V + C2V + C3V + ... € • What area plate separated by a gap of 0.10 – Generally, C C C C ... mm would create a capacitance of 1.0 F? eq = 1 + 2 + 3 + 17 18 € 3 Dielectrics Dielectrics • In real life, capacitor plates are not naked, the gap is filled with a dielectric material – Dielectrics are insulators. – Keeps plates separated, easier to build. – Also increases the capacitance • The dielectric constant – Isolated capacitor: insert dielectric, E is reduced by 1/κ • κ = the dielectric constant • C = κCo 19 20 Electrical Energy Storage Electrical Energy Storage • Graph V vs. q: • A defibrillator is used to deliver 200 J of V Slope = 1/C energy to a patient’s heart by charging a bank of capacitors to 750 volts. What is the capacitance of the defibrillator? Q • What is the area under the curve? 1 Q2 1 U = QV = = CV 2 2 2C 2 21 22 € 4 .